🧮 MPI Matrix Multiplication Lab

🔧 System Configuration

• Number of Processes: Choose 2, 4, 6, or 8 MPI processes. More processes = better parallelization for larger matrices.
• Matrix Size: Select 4×4, 6×6, or 8×8 matrices. Larger matrices demonstrate parallel efficiency better.
• Matrix Values:
  • Random Values: System generates random numbers (0-9) for matrices A and B
  • Manual Edit: Click on matrix cells to edit values manually for testing
• Animation Speed: Control visualization speed (0.25x to 3x) to match your learning pace.
• Execution Mode:
  • Automatic: Watch the complete parallel algorithm execution
  • Step-by-Step: Manually progress through each phase of the algorithm

📊 MPI Matrix Multiplication Algorithm

1. Phase 1 - Data Distribution (Scatter):
   • Master process (rank 0) divides matrix A into row blocks
   • Each worker process receives assigned rows + complete matrix B
   • Row distribution shown by color coding on matrices
2. Phase 2 - Parallel Computation:
   • Each process computes its assigned rows of result matrix C
   • Processes work independently and simultaneously
   • Matrix cells light up as calculations complete
3. Phase 3 - Result Collection (Gather):
   • Master process collects computed row blocks from all workers
   • Final result matrix C is assembled and displayed
   • Performance comparison shows parallel vs sequential timing

🎮 Using the Simulation

• Basic Workflow:
  1. Configure processes and matrix size
  2. Choose random or manual matrix values
  3. Select automatic or step-by-step mode
  4. Click "Start Simulation" to begin
• Manual Matrix Editing:
  • Switch to "Manual Edit" mode
  • Click any cell in matrices A or B to edit values
  • Use "Randomize Matrices" to generate new random values
• Step-by-Step Mode:
  • Click "Next Step" to progress through each phase
  • Read detailed logs for each operation
  • Perfect for understanding the algorithm step-by-step

📈 Understanding the Visualization

• Process Grid: Shows all MPI processes with their current status and assigned work
• Process Colors: Each process has a unique color that matches its assigned matrix rows
• Matrix Color Coding: Rows in matrices are colored to show which process handles them
• Process States:
  • Idle: Process waiting for work assignment
  • Computing: Process actively calculating matrix operations
  • Communicating: Process sending/receiving data
  • Completed: Process finished its assigned work
• Matrix Cell Animation: Cells light up as calculations complete, showing real-time progress

🚀 Parallel Computing Concepts

• Data Parallelism: Same operation (matrix multiplication) applied to different data chunks
• Load Balancing: Work distributed evenly among processes (rows per process ≈ matrix_size / num_processes)
• Communication Overhead: Time spent sending/receiving data between processes
• Scalability: Performance improvement with more processes (ideally linear speedup)
• Master-Worker Pattern: Rank 0 coordinates work distribution and result collection

📊 Performance Analysis

• Speedup: How much faster parallel execution is compared to sequential
• Efficiency: How well the parallel algorithm uses available processors
• Communication vs Computation: Ratio of time spent communicating vs calculating
• Optimal Process Count: Point where adding more processes doesn't improve performance
• Matrix Size Impact: Larger matrices typically show better parallel efficiency

🎯 Recommended Experiments

1. Basic Parallel Execution:
   • Start with 4 processes and 6×6 matrix
   • Use automatic mode to see full algorithm flow
   • Observe how work is distributed and collected
2. Scalability Testing:
   • Run same matrix size with 2, 4, 6, and 8 processes
   • Compare execution times and efficiency
   • Find optimal process count for different matrix sizes
3. Matrix Size Impact:
   • Use fixed process count (4) with different matrix sizes
   • Observe how parallel efficiency changes with problem size
   • Larger matrices should show better speedup
4. Algorithm Understanding:
   • Use step-by-step mode with manual matrix values
   • Create simple test cases (like identity matrix)
   • Verify results and understand each phase
5. Communication Analysis:
   • Use slow animation speed to observe communication patterns
   • Compare communication overhead with different process counts
   • Understand when communication becomes a bottleneck

💾 MPI Code Download

• Complete Implementation: Download working MPI C code for matrix multiplication
• Ready to Compile: Includes all necessary MPI functions and proper error handling
• Educational Comments: Detailed explanations of each code section
• Compilation Instructions: How to compile and run with mpicc and mpirun
• Performance Measurements: Built-in timing functions to measure speedup

🔍 Key Observations

• Load Distribution: Notice how rows are divided among processes (shown by colors)
• Parallel Efficiency: More processes don't always mean faster execution (overhead matters)
• Communication Patterns: Master-worker communication in scatter and gather phases
• Synchronization: All processes must complete before final result assembly
• Matrix Properties: Multiplication requires A rows × B columns operations
• Memory Distribution: Each process needs its assigned A rows + complete matrix B

❓ Common Questions

• Q: Why use more processes than CPU cores? A: Educational purposes - shows communication overhead effects
• Q: Why do cells light up at different times? A: Visualizes parallel computation happening simultaneously
• Q: What if processes > matrix rows? A: Some processes remain idle (realistic scenario)
• Q: Why is sequential sometimes faster? A: Small matrices have high communication-to-computation ratio
• Q: How does this relate to real HPC? A: Same principles apply to supercomputers with thousands of cores